Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.
Fatou Dust
See also
Julia Set, Fatou SetExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Fatou Dust." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FatouDust.html